J. Phys. Chem. 1993,97, 8132-8735
8732
Heats of Formation of SiHmClnCalculated by ab Initio Molecular Orbital Methods Ming-Der Su and H. Bernhard ScMegel' Department of Chemistry, Wayne State University, Detroit, Michigan 48202 Received: February 22, I993
Optimized geometries and vibrational frequencies for SiH,Cl, were calculated at the MP2/6-3 lG(d,p) level. Energy differences were computed at the MP4/6-3 1+G(2df,p) level (all structures) and the G-2 level (structures containing no more than two chlorines). The heats of formation of SiH,Cl, were estimated using the following isodesmic and isogyric reactions: [ (4 - n)/4]SiH4 ( 4 4 ) Sic14 -,SiHhnCl,, SiH, SiHhCl, SiHWnC1, SiH4, 3/4Si '/4H2 SiH3Cl- Sic1 '/2H + 3/4SiH4, '/2Si '/zH2 + SiH+nCl, SiHz-,Cl+ H + '/2SiH4, and l/4Si '/2H SiH&,Cl, SiH3&1, '/4H2 l/qSiH4. The calculated heats of formation (kcal/mol; 298 K, 1 atm) are as follows: SiC1, 36.5 f 1.5; SiHCl, 15.0 f 1.5; SiCl2, -38.6 f 1.5; SiHzCl, 8.0 f 1.5; SiHCl2, -34.0 f 1.5; SiCl3, -75.8 f 1.5; SiH3C1, -32.0 f 1.5; SiH2C12, -74.2 f 1.5; SiHC13, -1 16.8 f 1.5 (based on experimental values for SiH, and SiCl4). The present study uses a significantly higher level of theory than that used in earlier work and confirms the heats of formation predicted by the best previous theoretical studies to within f0.8 kcal/mol. The theoretical heats of formation are within the error bars of the most recent experimental values except for Sic1 (46 f 5 kcal/mol), suggesting that a new experimental value would be desirable for SiC1.
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+
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Introduction
Chlorosilanes are important reagents in chemical vapor deposition processes used in the semiconductor industry,l and reliable heats of formation are essential for any discussion of the mechanistic details of chemical vapor deposition. The thermochemistry of small silicon compounds has been the subject of a number of recent reviews.213 The heats of formation of the chlorosilanesare fairly well-known experimentally,and reasonable experimental estimates are available for the subchlorides, SiC1.. The thermochemistry of SiH,Cl, has also been the subject of a number of theoretical studies.'-' In general there is good agreement between the recent experimentaland theoreticalvalues. In thecourseof a study of the pathwaysfor thermaldecomposition of chlorosilanes,8we had the opportunity to re-examine the heats of formation of SiH,Cl,, (n + m = 1-4) at a higher level of theory than that used in previous studies. The heat of formation of tetrachlorosilane has been measured directly from the heat of chlorination of silicon? Farber and SrivastavalO determined AHfo for SiHkmC1, and SiCl, from effusion/mass spectroscopy studies. Walsh et a1.2bJ1obtained PHfO(SiC13) from SiHCl3 I, calling into question the value from the effusion/mass spectrometric study. Experimental estimates of AHfo(SiCl) are also available from spectroscopic studied2 and from studies on Si+ SiC14.13 Theoretical studies on the heats of formation of SiH,Cl, have been carried out with the bond additivity method at the MP4/ 6-31G(d,p) level (BAC-MP4) with4 and without5 bond length or spin corrections. These estimates are expected to have error bars of f 3 kcal/mol. Heats of formation have also been computed using isodesmic reactions at the MP4/6-3 1G(d) leve1.6~7Both sets of calculationssupport Walsh's value for AiYf(SiCl3). Good agreement with experimental is also found for SiH&l. and S i c k but Sic1 is calculated to be 10 kcal/mol more stable than inferred experimentally.
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Computational Method
Ab initio molecular orbital (MO) calculations were carried out with the GAUSSIAN 92 series of pr0grams.1~ Geometries were fully optimized using analytical gradients by second-order Mailer-Plesset perturbation theory with the 6-3 lG(d,p) basis set.15 Vibrational frequencies, zero-point energies, and thermal 0022-3654/93/2097-8732$04.00/0
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corrections (298 K, 1 atm) were calculated at the MP2/6-31G(d,p) levels using analytical second derivatives.16 Energy differences for isodesmic reactions were computed by fourth-order Maller-Plesset perturbation theory" (MP4SDTQ, frozen core) with the 6-31+G(2df,p) basis set and the G-2 level of theory.ls In the G-2 method,I8the energy computed at MP4/6-3 1lG(d,p) is corrected for the effect of diffuse functions obtained at MP4/ 6-31 l+G(d,p) and MP2/6-311+G(3df,2p), for the effect of higher polarization functions obtained at MP4/6-3 1lG(Zdf,p) and MP2/6-3 11+G(3df,2p), and for the effect of electron correlation beyond fourth-order obtained at QCISD(T)/6-3 11G(d,p). The average absolute error of the additivity assumptions in the G-2 level of theory is only 0.30 kcal/mol.18b Higher level corrections for deficienciesin the energy are estimated empirically by comparing with well-established atomization energies, ionization energies, electron affinities, and proton affinities. At the G-2 level of theory, the mean absolute error in these energy differences is 1.3 kcal/mol.18 A similar level of accuracy can be expected in the present study. Because of computational cost, the G-2 level was used only for molecules containing at most two chlorines.
Results and Discussion The calculated total energies, zero-point energies, and thermal corrections are listed in Table I. The optimized geometries are given in Table 11. The MP2/6-31G(d,p) optimized S i 4 1 bond lengths are ca. 0.005-0.010 A shorter than the HF/6-31G(d) values. The valence angles and Si-H bond lengths are within 0.5' and 0.005 Aof the HF/6-31G(d) values. Theexperimental and theoretical vibrational frequenciesare listed in Table I11and plotted in Figure 1. The calculated harmonic frequencies are ca. 6% too high, primarily due to the neglect of vibrational anharmonicity. Figure 1 shows a very good linear correlation between theory and experiment (R2 = 0.997). Theonlysignificant exceptions are the Si-H stretching modes in SiH3. An earlier assignment19 of the SiH3 spectrum has been questioned.2s24 Accurate experimental values are available for the umbrella and degenerate deformation modes,21J2 but the Si-H stretchingregion is difficult to observe directly because of overlap with SiH4. The present MP2 calculations and previous studies5a.24 predict the symmetric and degenerate stretches at 2140-2150 and 21802190cm-1,respectively. IftheSi-HstretchesofSiH3aredropped, 0 1993 American Chemical Society
Heats of Formation of SiH,Cl,
TABLE I:
The Journal of Physical Chemistry, Vol. 97, No. 34, 1993 8733
Total Energies’
molecule SiH (211) SiCl(2II) SiHz (‘AI) SiHCl(’A‘) Sic12 (‘AI) SiH3 (zA1) SiH2CI (2A‘) SiHC12 (2A’) Sic13 ( z A ~ ) SiH4 SiH3Cl SiH2C12 SiHC13 Sic&
6-31G(d,p) MP2 -289.481 22 -748.587 25 -290.093 98 -749.195 37 -1208.301 79 -290.708 70 -749.792 19 -1208.878 38 -1667.964 35 -291.349 86 -750.434 14 -1209.520 71 -1668.607 26 -2127.691 64
6-31+G(2df,p) MP2 -289.489 -748.643 -290.106 -749.255 -1208.409 -290.721 -749.852 -1208.986 -1667.120 -291.364 -750.496 -1209.630 -1668.765 -2127.897
MP4 -289.514 -748.684 -290.134 -749.300 -1208.472 -290.748 -749.896 -1209.048 -1668.199 -291.396 -750.545 -1209.696 -1668.848 -2127.997
97 35 22 01 87 20 34 56 54 78 47 82 26 26
MP2/6-3 lG(d,p) ZPE thermal
G-2 04 74 49 33 01 64 98 53 97 56 32 86 59 99
-289.546 -748.768 -290.167 -749.385 -1208.610 -290.773 -749.975 -1209.181
3.07 0.78 7.77 5.10 1.84 14.07 10.99 7.38 3.32 20.57 17.31 13.54 9.31 4.8 1
00 62 71 96 39 51 83 95
-291.419 04 -750.621 81 -1209.828 17
1.48 1.60 1.80 1.94 2.37 1.87 2.04 2.49 3.18 1.90 2.10 2.56 3.22 3.99
Total energies in atomic units (1 au = 627.51 kcal/mol), zero-point energies (ZPE) and thermal energies (298 K, 1 atm) in kilocalories pcr mole; G-2 values for SiH, and Sic1 from ref 18. Note that the definition of the G-2 energy includes ZPE.
TABLE
II: MP2//631C(d,p) Optimized Geometries’
molecule symmetry R(SiH) R(SiC1) LHSiH LHSiCl LClSiCl SiH
Sic1 SiH2 SiHCl SiClz SiH3 SiHzCl SiHClz Sic13 SiH4 SiHqCl SiH& SiHCl3 Sic&
c,, C-,
cz, C, CZ,
Ck C, C,
1.515 2.072 1.508 1.509 1.473 1.472 1.473
c 3 0
Td
--
CZ,
9,
1.472 1.468 1.463 1.459
Td
92.33 2.077 2.073
95.25 101.7 111.2 111.0
2.056 2.047 2.043 2.056 2.042 2.032 2.025
109.1 108.3
110.3 112.5
108.6 108.5 109.2
110.8 109.7 110.5 109.7
~
molecule
~
~
~~~
~~~
frequencies (cm-I)
2144 (1970) 547 (534) 1078 (1004), 2178 (1964), 2178 (1973) 545 (522), 859 (808), 2162 208 (202), 540 (502), 540 (514) 822 (723), 985’ (8709,2325 (1955), 2362’ (1999’) 569,680,781,976,2324,2359 185,538,608,700,802,2327 171’, 253,494 (470), 617’ (582’) 974‘’ (913”), 1018’ (9723,2348 (2186), 2360” (2189”) Sifi SiH3Cl 572 (551), 691’ (663’), 1003’ (952’), 1016 (945), 2366 (2201), 2382’ (221 1’) SiH2C12 193 (188), 548 (527), 617 (590), 623 (602), 746 (710), 936 (876), 1008 (954), 2390 (2224), 2408 (2237) SiHCl3 180‘(176’), 262 (254), 511 (499), 628‘ (6009,852’ (81 l’), 2420 (2261) SiCh 151’ (149’), 229” (220‘3,434 (425), 647” (620”) SiH Sic1 SiH2 SiHCl Sic12 SiH3 SiHzCl SiHCl2 Sic13
Experimental (anharmonic) values in parentheses;doubly degenerate marked with a prime; triply degenerate marked with a double prime.
a scale factor of 0.945 f 0.002 is obtained at the MP2/6-31G(d,p) level. A similar value (0.93) was found in HF/6-31G(d) calculations on SiH,Cln5 (frequencies below 1900 cm-1 only) and SiH,FnZ5 (all frequencies). Table IV summarizes the enthalpy differences for three sets of isodesmic and isogyric reactions used in the estimation of the heats of formation of SiH,Cl,. The first set interpolatesbetween SiH, and SiC1,.
m-n
+
-
2000
3000
MP2/6-310* harmonic frequencies
TABLE IIk MP2/631G(d.p) Vibrational Freauencies’ ~~
1000
0
I, Bond lengths in angstroms; angles in degrees.
-SiH, %Cl, SiH,Cl, m m Since the experimental AHfo of SiH4 and Sic14 are firmly established? this reaction is used to estimate the heats of formation
Figure 1. Comparisonofexperimentalanharmonicvibrationalfrequencies and MP2/6-31G(d,p) calculated harmonic vibrational frequencies.
of SiHsCl, SiH2C12, and SiHCl3. The experimental and theoretical AHfo of SiH, SiHz, and SiHs are in close but the experimental AHfo of SiCl, SiC12, and SiClp are less well-known.2 Hence, a different set of reactions must be used. Given the AHf” of SiH, SiH2, and SiH3, the heats of formation of SiC1, SiHCl, SiClz, SiH2C1, SiHCl2,and Sic13can be computed by transferring the chlorines from SiH&l,. SiH,
+ SiH,Cl,
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SiH,,Cl,
+ SiH,
(2) Previous studies have used the bond additivity method4.s to estimate the AHfo of SiH,Cl, at the MP4/6-31G(d,p) level of theory. Cast into the form of an isodesmic reaction, the bond additivity method uses the following reaction to compute the heat of formation:
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4-m-n Si + YSiH, %iCl, SiH,Cl, (3) 4 4 Thisassumesthat the corrections for a given bond are independent of the number and nature of the other substituents. There is some evidence that a variety of properties, including the energy, are not linear with the number of halogen substituents.6 Since reliable values for the AHfo of SiHk,Clncan be determined from (l), reaction 3 can be modified to keep the number of chlorines bonded to a silicon the same in reactants and products: 4-m-n 4 Si
4-m-n SiH, 4 (4) Although reactions 3 and 4 are isodesmic, they are not isogyric (Le. reactants and products do not have the same number of unpaired electrons). This can be remedied by adding the
+ ~SiH,,Cl,
SiH,Cl,
8734 The Journal of Physical Chemistry, Vol. 97, No. 34, 1993
Su and Schlegel
TABLE Iv: Isodesmic Reactions' 6-31G(d,p)
6-3 l+G(2df,p)
--
reaction MP2 MP2 MP4 G-2 eXDtb I/zSiHz + 1/2SiC12 SiHCl 1.73 2.05 1.98 1.80 2/3SiH3+ l/3SiC13 SiH2Cl 1.32 1.41 1.56 I/,SiH, + 2/3SiC13 SiHClz 0.70 0.71 0.85 1.15 1.31 1.42 -0.5 )/&iH4 + l/&iC4 SiH3CI 0.86 -1.5 l/zSiH4 + '/2SiC4 SiHzC12 0.63 0.73 l/&iH, + 3/&iC14 SiHCl3 -0.15 -0.19 -0.09 -1.9 SiH + SiHsCl Sic1 + SiH4 -12.15 -12.11 -12.87 -12.54 -1 .o SiHz + SiH3Cl- SiHCl + S i b -10.20 -10.19 -10.18 -9.77 SiHz + SiHzC12 Sic12 + S i b -22.18 -22.59 -22.35 -21.14 -21.0 SiH3 + SiH3Cl- SiHzCl + SiH4 0.66 0.51 0.42 0.25 SiH3 + SiHzClz SiHClz + SiH4 1.03 0.73 0.56 0.39 SiH3 + SiHCl3 Sic13 + SiH4 1.60 1.22 0.94 -1.2 3/&1 + '/4HZ + SiH3CI Sic1 + l/zH + 3/&iH4 20.70 19.92 19.73 19.73 31.4 l/zS1+ l/zHz + SiH3CI SiHCl + H + l/zSiH, 49.5 1 48.08 48.49 48.86 36.32 31.49 38.1 l/2Si + I/zH2 + SiHzClz Sic12 + H + I/2SiH4 37.53 35.68 I/&! + I/zH + SiH3CI SiHzCl+ '/4& + */&iH4 -9.30 -9.49 -9.92 -10.88 l/&i + l/2H + SiHzClz SiHClz + '/4H2 + l/&i& -8.92 -9.27 -9.78 -10.74 l/&i + l/zH + SiHCI3 Sic13 + '/4HZ + l/&iH4 -8.35 -8.78 -9.40 -8.7 a Calculated enthalpy differences (298 K, 1 atm) in kilocalories per mole. * Using the experimentalheats of formation listed in Table V (first entry is used in caw where there is more than one value).
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-- ---
TABLE V Heats of Formation and Entropies' molecule SiH Sic1 SiHz SiHCl Sic12 SiH3 SiH2Cl SiHCl2 Sic13
SiH4 SiH3CI SiHzClz SiHCl3 Sic4 e
expt M f Z 9 8
** 1.6d * -40.3 * 0.8$-39.4 3.4' 47.9 * 0.6d -80.1 * 2.2f 8.2 0.9 -33.9 * 2,8-32.4 i 2 . 9 -76.6 38-75.3 * 2h -118.6 1.5,8-119.3 k 1 . 9 -158.4 * i.3r
present calc AHfoBa
89.6 1.2b 46 5; 47.4 65.5 1.W
36.5 15.0 -38.6 8.0 -34.0 -75.8
-32.0 -74.2 -1 16.8
previous calc AHfo2m 91.7,'91.0) 89.9: 87.8' 37.9,' 31.8) 36.6" 68.1,'64.8) 65.7,' 62.4' 17.0,'lS.W -37.6,' -36.2) -38.9" 41.8,'41.4) 47.1: 46.7' 7.8,' 7 . 9 -34.3,'-34.01 -76.5,'-76.4) -76.4" 6.g -32.2,'-32.01 -74.5,'-14.@ -117.0,'-117.11
~ a lSa8 c 46.0 55.6 50.9 59.9 68.5 53.9 62.4 70.5 75.9 53.7 61.9 69.6 76.8 83.9
* 298 K, 1 atm; enthalpies in kilocalories per mole, entropies in calories per mole Kelvin. Reference 26. Reference 13. References 9, and loa. Reference 21. IReferences 2a. and 11.8 Reference 9. * Reference lob. Reference 5. 1 Reference 4. k Reference 25. 1Reference 18. Reference 7.
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appropriate multiple of the reaction HZ balance the number of unpaired spins:
2H to reaction 4 to
+ '/4H2 + SiH3Cl- Sic1 + l/zH + 3/4SiH4 1/2Si + '/zHz + SiH,Cl, SiH,CI, + H + '/$iH4 '/4Si + l/zH + SiH,,Cl, SiH,,Cl, + 1/4H2+ 1/4SiH4 3/4Si
-
(5) Although not as simple as reaction 2, reaction 5 has the advantage that the AHfofor SiH,Cl, can be computed without reference to the AHfo for SiH, SiHz, and SiH3. For the reactions collected in Table IV, there is generally very good agreement among all of the levels of theory listed (including MP2/6-3 lG(d,p)). The average absolutedifference between the MP4/6-31G(2df.p) and G-2 energies is 0.5 kcal/mol; the largest difference is 1.2 kcal/mol for SiC12. This level of agreement illustrates the capabilities of carefully selected isodesmic and isogyric reactions, and validates earlier calculations of the heats of formation of SiH,F, based on similar isodesmic reactions.25 The final estimates of the AHfo for SiH,-,,Cl,, listed in Table V, are obtained from reaction 1 using the MP4/6-31+G(Zdf,p) energies; the AHfofor the remaining SiH,Cl, are calculated as an average of the values obtained from reactions 2 and 5 using the G-2 energies for SiCl, SiHC1, SiCl2, SiH2C1, and SiHCl2 and the MP4/6-31 +G(2df,p) energies for SiC13. The estimated error in the heats of formation is f1.5 kcal/mol. The AHfofor SiCl, are within 0.6 kcal/mol of the values obtained from isodesmic reactions at the MP4/6-3 1G(d,p) level? Thevalues for S i L C 1 ,
and SiH&l, are within 0.7 kcal/mol of the BAC-MP4 cal~ulations.~*5 The differences for SiC12, SiHCl, and Sic1 are somewhat larger but are still inside the f 3 kcal/mol error estimated for BAC-MP4. Most of the present calculations are within the error bounds of the experimental heats of formation, with the exception of Sic1and Sic&. In a kineticidnation study, WalshzbJ1measured Do(C13Si-H) = 91.3 f 1.5 kcal/molandobtainedAHto298(SiC13) = -80.1 f 2.2 kcal/mol using AHr0298(SiHC13) = -1 19.3 f 1.6 kcal/mol. The present calculations give Do(C13Si-H) = 93.1 kcal/mol and AHfo298(SiHCl3)= -1 16.8 kcal/mol. Thus, the apparent discrepancy for Sic13 is due to the value used for the heat of formation of SiHC13. Since isodesmic reaction 1 is quite reliable, especiallyat the level of theory used in the present work, the calculated heat of formation of SiHCl3 can be combined with the measured Do(C13Si-H) to yield AHf0298(SiCl3) = -77.6 f 2.5 kcal/mol. The experimental A H f O 2 9 8 for Sic1 has been questioned previou~ly.~-~.~ Mass spectral/effusion studies give 47.4 f 1.6 kcal/mol;lO. analysis of spectroscopic data yields 32,33, and 43 kcal/mol;12 thresholds for Si+ + S i c 4 Sic1 + Sicla+ give 46 i 5 kcal/mol.13 On the basis of the available data, WalshZb recommended 37 f 10 kcal/mol "with caution but not with great confidence". Theoretical calculations consistently predict a heat of formation in the range of 36-38 kcal/m0L3 Until an accurate value for heat of formation for Sic1 can be determined experimentally, the present theoretical estimate, AHf0z98(SiC1)= 36.5 f 1.5 kcal/mol, is recommended.
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Heats of Formation of SiH,Cl,
The Journal of Physical Chemistry, Vol. 97, No. 34, 1993 8735
Acknowledgment. We wish to thank the Pittsburgh Supercomputer Center for generous allocations of computer time. This work was supported by a grant from the National Science Foundation (CHE 90-20398).
(13) (a) Weber, M. E.; Armentrout, P. B. J. Phys. Chem. 1989,93,1596. (b) Fisher, E. R.; Armentrout, P. B. J. Phys. Chem. 1991, 95,4765. (14) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.;Gompcrts, R.; Andres, J. L.; Raghavacbari, K.; Binkley,
References and Notes
J. J. P.; Pople, J. A. GAUSSIAN 92; Gaussian, Inc.: Pittsburgh, PA, 1992. (15) (a) Hariharan, P. C.; Pople, J. A. Theor. Chem. Acra 1973,28,213, and references cited therein. (b) Franc], M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.; Gordon, M. S.; DeFrees, D. J.; Pople, J. A. J. Chem. Phys. 1982, 77,3654. (c) Frisch, M. J.; Pople, J. A.; Binkley, J. S.J. Chem. Phys.
J.S.;Gonzalez,C.;Martin,R.L.;Fox,D.J.;Defrees,D.J.;Baker,J.;Stewart, (1) For some leading references, see: (a) Jasinski, J. M.; Gates, S.M. Ace. Chem. Res. 1991,24,9. (b) Jasinski, J. M.; Meyerson, B. S.;Scott, B. A. Annu. Rev. Phys. Chem. 1987,38,109. (c) Jensen, K. F. Adu. Chem. Ser. 1989, 221, 199. (2) (a) Walsh, R. In The Chemistry of Organic Silicon Compounds; Patai, S., Rappport, Z., Eds.; Wiley: New York, 1988. (b) Walsh, R. J. Chem. Soc.,Faraday Trans I 1983,79,2233. (c) Doncaster, A. M.; Walsh, R. J.Chem. Soc.,Faraday Trans 2 1986,82,707. (d) Walsh, R. Ace. Chem. Res. 1981, 14, 246. (3) Gordon, M. S.;Francisco, J. S.;Schlegel, H. B. Adv. Silicon Chem. 1993, 2, 137. (4) (a) Ho. P.; Melius, C. F. J . Phys. Chem. 1990,94,5120. (b) Allendorf, M. D.; Melius, C. F. J. Phys. Chem. 1993, 97, 720. ( 5 ) Ho, P.; Coltrin, M. E.; Binkley, J. S.;Melius, C. F. J. Phys. Chem. 1985,89,4647; 1986, 90, 3399. (6) Ignacio, E. W.; Schlegel, H. B. J. Phys. Chem. 1992, 96, 5830. (7) Darling, C. L.; Schlegel, H. B. J. Phys. Chem. 1993, 97, 1368. (8) Su,M.-D.; Schlegel, H. B. J . Phys. Chem., in press. (9) Chase,M. W.;Davies,C.A.;Downey,J.R.;Frurip,D. J.;McDonald, R. A.; Szverud, A. N. JANAF Thermochemical Tables, 3rd ed. J. Phys. Chem. Ref. Dora 1985, 14. (10) (a) Farber, M.; Srivastava, R. D. J. Chem. Thermodyn. 1979, I I , 939. (b) Farber, M.; Srivastava, R. D.Chem. Phys. Leu. 1979, 60, 216. (11) Walsh, R.; Wells, J. M. J . Chem. Soc., Faraday Trans I 1976, 72, 1212. (12) (a) Gaydon, A. G. Dissociation Energies and Spectra of Diatomic Molecules; Chapman and Hall: London, 1969. (b) Kuzyakov, Y. Y. Vestn. Mosk. Univ. 1969, 23, 21. (c) Singhal, S.R.; Verma, R. D. Can. J . Phys. 1971, 49, 407.
1984,80, 3265, and references cited therein. The 6-31G(d) and 6-31G(d,p) basis sets are the same as 6-31G* and 6-31G**, respectively. (16) (a) Pople, J. A.; Krishnan, R.; Schlegel, H. B.; Binkley, J. S . Inr. J. Quantum Chem. Symp. 1979, 13, 225. (b) Trucks, G. W.; Frisch, M. J.; Head-Gordon, M.; Andres, J. L.; Schlegel, H. B.; Salter, E. A. J. Chem. Phys., submitted for publication. (17) (a) Mnller, C.; Plesset, M. S.Phys. Reu. 1934,16, 618. (b) For a review, see: Bartlett, R. J. Annu. Rev. Phys. Chem. 1981, 32, 359. (18) (a) Curtiss, L. A.; Raghavachari, K.; Trucks, G. W.; Pople, J. A. J . Chem.Phys. 1991,94,7221. (b) Curtiss,L. A.;Carpenter,J. E.;Raghavachari, K.; Pople, J. A. J. Chem. Phys. 1992, 96, 9030. (19) Milligan, D. E.; Jacox, M. E. J . Chem. Phys. 1970, 52, 2594. (20) Fredin, L.; Hauge, R. H.; Kafafi, Z. H.; Margrave, J. L. J. Chem. Phys. 1985,82, 3542. (21) Yamada, C.; Hirota, E. Phys. Reu. Letr. 1986,56, 923. (22) Johnson, R. D.; Tsai, B. P.; Hudgens, J. W. J . Chem. Phys. 1989, 91, 3340. (23) Abouaf-Marguin, L.; Lloret, A.; Oria, M.; Saudi, B. Chem. Phys. 1988,127, 385. (24) Allen, W. D.;Schaefer, H. F., 111. Chem. Phys. 1986, 108, 243. (25) Ignacio, E. W.; Schlegel, H. B. J. Chem. Phys. 1990,92, 5404. (26) Berkowitz, J.;Green, J. P.; Cho, H.;Ruscic, B.J. Chem. Phys. 1987, 86, 1235. (27) Moffat, H. F.; Jensen, K. F.; Carr, R. W. J. Phys. Chem. 1991,95, 145. (28) Pople, J. A.; Curtiss, L. A. J . Phys. Chem. 1987, 91, 155, 3637.
